Trans RINA, Vol 152, Part A4, Intl J Maritime Eng, Oct-Dec 2010
gravity in the specified direction. Thus, for example, xp - xg represents the distance from the vessel’s centre of gravity to the replenishment point in the x direction. For this study, surge, sway and yaw are neglected and hence these terms are reduced to give the following equation set which are non-dimensionalised with respect to the wave amplitude, ζ.
Δη ζ
Δη ζ
x' 1 ( z z ) 1
y'
=− =− −
( z z ) =+ −
Δ ηη η ζ
z' 1⎡⎤ ⎣⎦
pg 5 pg 4 3p g
( y y ) 4 −( x x ) 5 p − g Using equation (8), the non-dimensional relative
variations in separation were determined for conditions 1, 2 and 3, where the subscripts F and T represent the frigate and tanker respectively. In this equation, the three terms consider the instantaneous location of the RAS point on each vessel relative to the other. The RM’ was then determined over a given time-step. This method ensures that the phase relationship between the different vessel motions is considered.
RM' = (ΔxF − ΔxT ) + Δy −ΔyT ) + Δz − ΔzT ) ' ' 2 ( ' F ' 2 ( ' F ' 2 (8)
The RAS point locations used for the change in relative separation analysis are given in Table 3, relative to vessel midships, centreline and keel. The frigate aft RAS point was used for Conditions 1 and 2 while Condition 3 used the frigate forward RAS point.
Table 3: Location of RAS Points Frigate Tanker Aft Forward
x (m) from MS -6.45 28.20 y (m) from CL 6.85 6.85 z (m) from keel 10.77 10.77
The experimental
-17.58 15.5
10.77
The relative motion RAOs are shown in Figure 8 to Figure 10.
results show a small
increase in relative motion due to an increase in supply tanker displacement. Pitch clearly has more effect in Condition 3 compared to Conditions 1 and 2, given the use of the forward RAS point. This is demonstrated by the significant increase in relative motion with an increase in longitudinal separation. By using this forward RAS point, the distance between the CoG and the point used to calculate the relative motion is quite large; therefore pitch motion will result in a relatively large vertical displacement at the RAS.
Overall these plots show a relatively poor correlation between predictions and experiments; with the numerical
results under predicting the relative motions by approximately 50%. The lower magnitude may
be
attributable to the under prediction of the frigate’s roll, the dominant vessel motion. The predictions appear to exhibit very similar resonant frequencies to those found experimentally;
though several additional peaks are
apparent at higher frequencies. These peaks in the data are probably due to the large oscillations in the frigate heave and pitch RAOs.
(7)
To date no full scale data for vessel motions during RAS operations have been
obtained, mainly since its
acquisition would require a major effort to overcome a variety of technical and logistical issues. However in the future it may provide additional data for validation purposes.
Classification Society rules, for example [20], governing RAS operations state that only the dynamic behaviour of the supplying ship needs to be considered when designing RAS systems. It is clear from this work, and a previous study [15] that the motions of the receiving ship should also be accounted for during the design process.
5. VESSEL RESPONSES IN IRREGULAR SEAS
To ascertain the effect of longitudinal separation on the responses of the vessels in a realistic seaway, wave spectra
were applied to both the numerically and
experimentally derived RAOs. Four different sea states were modelled using the two-parameter Bretschneider (ITTC) spectrum in accordance with the DEF (AUST) 5000 Materiel Requirement Set [21] for seakeeping to represent the mean of sea states 3, 4, 5 and 6 (Table 4). The significant wave height and period combinations of these spectra are based on the typical conditions in the waters around Australia, so that these sea states represent the range of typical sea conditions experienced during RAS operations.
Table 4: Sea State Parameters [21]
Sea State Significant Wave Height
(m)
3 0.875 4 1.875 5 3.25 6 5.00
The motions of
Modal Period (sec)
8.9
10.3 11.7 12.8
the vessels in irregular seas were
examined in terms of the extreme displacement with 1 percent exceedence probability in 3 hours [22] with the tanker in full load condition. A time period of 3 hours was chosen since this is a typical duration of a RAS operation.
©2010: The Royal Institution of Naval Architects
A-187
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74